Welcome to the website of the APDE group in Bilbao (at BCAM and EHU) working in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and related topics.
EHU, October 1st, 2026, 12:00 - 13:00
Long-wave instability of periodic shear flows with constant magnetic field for the 2D resistive MHD equations.
Claudia Peña (BCAM)
The purpose of this talk is to present the article [1] in which we establish two results:
On the one hand, we study the long-wave linear (in)stability of the two-dimensional viscous, resistive Magnetohydrodynamic (MHD) equations on the periodic domain T_\alpha × T = R/(2π\alpha Z) × R/(2πZ) in the regime α ≪ 1, around a periodic shear flow (U(y), 0) coupled with a constant background magnetic field b = (b1, b2). It is a non-trivial extension of the recent paper [2] for the Navier-Stokes equations to the MHD setting.
On the other hand, as a dynamical consequence of the spectral analysis carried out along the proof, we obtain a splitting of the phase space into unstable and stable subspaces, on which solutions grow or decay exponentially in Sobolev norm.
[1] Feola, R., Franzoi, L., Montalto, R., Peña, C. Long-wave instability of periodic shear flows with constant magnetic field for the 2D resistive MHD equations. arXiv:2607.25836.
[2] Colombo, M., Dolce, M., Montalto, R. and Ventura, P.: Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations. arXiv:2509.18070.
Current organizers: Daniel Eceizabarrena (BCAM), Mikel Florez (EHU), Arnab Roy (BCAM).